Marketing Mix Modeling project by Sokolov Alexander

import mmm_pyton 

import plotly.graph_objects as go
import pandas as pd
import numpy as np
import statsmodels.api as sm
import math 
from sklearn.base import BaseEstimator, TransformerMixin
from lmfit import Parameters, Minimizer, report_fit, Parameters
from sklearn.metrics import r2_score, mean_squared_error, median_absolute_error

import os
import json
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.api as sm

from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.impute import SimpleImputer
from sklearn.preprocessing import StandardScaler, LabelBinarizer
from sklearn.pipeline import Pipeline
from sklearn.linear_model import Lasso, Ridge, LinearRegression, ElasticNet
from sklearn.metrics import r2_score, mean_squared_error, median_absolute_error

from sklearn_pandas import DataFrameMapper, gen_features

from lmfit import Parameters, Minimizer, report_fit, Parameters

from scipy.optimize import minimize, Bounds, LinearConstraint

import random

dataset = pd.read_csv('Media_data.csv', sep = ';').dropna()

dataset

	Week	Sales	Brand_price	Average_category_price	TV_1	TV_2	TV_3	TV_4	TV_5	TV_6	TV_7	TV_8	TV_9	TV_competitor_1	TV_competitor_2	TV_competitor_3	TV_competitor_4	Press
0	04.01.2010	7092.0	55	104	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1	11.01.2010	8664.0	52	100	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	18.01.2010	7526.0	53	97	0	0	0	0	0	0	0	0	0	0	0	0	0	50
3	25.01.2010	9165.0	55	103	0	0	0	0	0	0	0	0	0	0	0	0	0	56
4	01.02.2010	8713.0	52	101	0	0	0	0	0	0	0	0	0	0	0	0	0	6
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
134	30.07.2012	9294.0	90	145	0	0	0	0	0	0	0	0	0	0	0	0	0	0
135	06.08.2012	9105.0	93	142	0	5	0	0	0	0	0	13	0	0	14	0	0	30
136	13.08.2012	9135.0	90	141	0	9	0	0	0	0	0	15	0	0	15	0	0	53
137	20.08.2012	9503.0	89	139	0	0	0	0	0	0	0	0	0	0	17	0	0	25
138	27.08.2012	8983.0	89	142	0	0	0	0	0	0	0	0	0	0	7	0	0	14

139 rows × 18 columns

Basic data manipulation and visualization

dataset['Week'] = pd.to_datetime(df['Week'])

month = df.groupby(df['Week'].dt.strftime('%B-%Y'))['Sales'].mean().sort_values()

Средние значения продаж в месяц

print(round(month))

Week
May-2010           7188.0
July-2010          7661.0
March-2010         7744.0
April-2010         7880.0
February-2010      8057.0
September-2010     8070.0
June-2010          8552.0
November-2012      8850.0
January-2010       9031.0
April-2012         9037.0
August-2010        9042.0
August-2012        9207.0
July-2012          9268.0
May-2012           9343.0
June-2012          9698.0
October-2010       9892.0
June-2011          9908.0
November-2010     10044.0
December-2010     10164.0
September-2011    10352.0
February-2012     10417.0
March-2012        10609.0
September-2012    10850.0
December-2011     11005.0
May-2011          11213.0
July-2011         11804.0
August-2011       11835.0
November-2011     11861.0
January-2012      11899.0
February-2011     12132.0
April-2011        12251.0
January-2011      12914.0
December-2012     13169.0
October-2011      13192.0
March-2011        13382.0
Name: Sales, dtype: float64

import warnings
warnings.filterwarnings('ignore')

import seaborn as sns

Cоотношение между ценой бренда и средней ценой категории

dataset['Brand_price'].corr(dataset['Average_category_price'])

0.9361923528387466

sns.distplot(dataset['Brand_price'], hist = False, kde = True,
                 kde_kws = {'shade': True, 'linewidth': 3})
sns.distplot(dataset['Average_category_price'], hist = False, kde = True,
                 kde_kws = {'shade': True, 'linewidth': 3})

<AxesSubplot:xlabel='Average_category_price', ylabel='Density'>

Гистограмма средних продаж в месяц за 2010-2011 гг.

price = df.groupby(df['Week'].dt.strftime('%Y-%m'))['Sales'].mean()

pricenew = price[:24]

pricenew.plot.bar()

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-3-b596aabfc2df> in <module>
----> 1 pricenew.plot.bar()

NameError: name 'pricenew' is not defined

Распределение по кварталам

price1 = df.groupby(df['Week'].dt.to_period('Q'))['Sales'].mean()

price1

Week
2010Q1     8358.583333
2010Q2     7872.857143
2010Q3     8424.230769
2010Q4    10054.923077
2011Q1    12853.307692
2011Q2    11130.923077
2011Q3    11451.000000
2011Q4    12091.857143
2012Q1    10856.272727
2012Q2     9359.166667
2012Q3     9724.100000
2012Q4    11009.500000
Freq: Q-DEC, Name: Sales, dtype: float64

price1.plot.bar()

<AxesSubplot:xlabel='Week'>

price2 = df.groupby(df['Week'].dt.to_period('w'))['Sales'].mean()

price2

Week
2009-12-28/2010-01-03     8933.5
2010-01-11/2010-01-17    10599.0
2010-01-18/2010-01-24     7526.0
2010-01-25/2010-01-31     9165.0
2010-02-08/2010-02-14     7779.0
                          ...   
2012-08-20/2012-08-26     9503.0
2012-08-27/2012-09-02    10579.0
2012-09-03/2012-09-09    10187.0
2012-11-05/2012-11-11     8850.0
2012-12-03/2012-12-09    13169.0
Freq: W-SUN, Name: Sales, Length: 119, dtype: float64

Q1 = price2[1:10]

Q1.plot.bar()

<AxesSubplot:xlabel='Week'>

Q2 = price2[10:21]

Q2.plot.bar()

<AxesSubplot:xlabel='Week'>

Q3 = price2[21:33]

Q3.plot.bar()

<AxesSubplot:xlabel='Week'>

Q4 = price2[33:45]

Q4.plot.bar()

<AxesSubplot:xlabel='Week'>

OLS

import statsmodels.formula.api as smf

ac = smf.ols(formula = 'Sales ~ Brand_price + Average_category_price + TV_1 + TV_2 + TV_3 + TV_4 + TV_5 + TV_6 + TV_7 + TV_8 + TV_9 + TV_competitor_1 + TV_competitor_2 + TV_competitor_3 + TV_competitor_4 + Press ', data=dataset).fit()
ac.params

Intercept                 2271.715702
Brand_price                 14.394308
Average_category_price      46.549117
TV_1                        19.981083
TV_2                        67.795773
TV_3                        20.366270
TV_4                        38.130762
TV_5                       -86.733684
TV_6                       -62.747017
TV_7                        57.276712
TV_8                       -73.160058
TV_9                      -137.411201
TV_competitor_1              5.744274
TV_competitor_2            -55.923583
TV_competitor_3             27.666143
TV_competitor_4            116.277123
Press                        7.251206
dtype: float64

ac.summary()

OLS Regression Results

Dep. Variable:	Sales	R-squared:	0.505
Model:	OLS	Adj. R-squared:	0.441
Method:	Least Squares	F-statistic:	7.794
Date:	Wed, 08 Sep 2021	Prob (F-statistic):	2.03e-12
Time:	09:03:42	Log-Likelihood:	-1211.9
No. Observations:	139	AIC:	2458.
Df Residuals:	122	BIC:	2508.
Df Model:	16
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
Intercept	2271.7157	1600.751	1.419	0.158	-897.130	5440.561
Brand_price	14.3943	36.130	0.398	0.691	-57.129	85.918
Average_category_price	46.5491	30.305	1.536	0.127	-13.443	106.542
TV_1	19.9811	7.922	2.522	0.013	4.299	35.663
TV_2	67.7958	46.223	1.467	0.145	-23.707	159.298
TV_3	20.3663	22.467	0.906	0.366	-24.110	64.842
TV_4	38.1308	8.423	4.527	0.000	21.456	54.805
TV_5	-86.7337	128.089	-0.677	0.500	-340.299	166.831
TV_6	-62.7470	193.136	-0.325	0.746	-445.078	319.584
TV_7	57.2767	114.434	0.501	0.618	-169.257	283.810
TV_8	-73.1601	96.965	-0.755	0.452	-265.111	118.791
TV_9	-137.4112	100.424	-1.368	0.174	-336.211	61.389
TV_competitor_1	5.7443	10.950	0.525	0.601	-15.932	27.421
TV_competitor_2	-55.9236	39.815	-1.405	0.163	-134.742	22.895
TV_competitor_3	27.6661	18.034	1.534	0.128	-8.034	63.366
TV_competitor_4	116.2771	25.792	4.508	0.000	65.220	167.334
Press	7.2512	7.391	0.981	0.328	-7.380	21.883

Omnibus:	17.106	Durbin-Watson:	0.827
Prob(Omnibus):	0.000	Jarque-Bera (JB):	21.613
Skew:	0.729	Prob(JB):	2.03e-05
Kurtosis:	4.267	Cond. No.	1.75e+03

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.75e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

MMM

from scipy.optimize import minimize, Bounds, LinearConstraint, curve_fit
import pysolnp

def opt_rev_plot(revenue_table):
    fig = go.Figure()
    fig.add_trace(go.Scatter(
            x=revenue_table['budget'].values,
            y=(revenue_table['profit'].values),
            name='optimal curve'
    ))
	
    fig.update_layout(title='Optimal ROAS curve',
                   xaxis_title='Yearly investments (mln rub)',
                   yaxis_title='Expected yearly ROAS in comparison')
	
    fig.show()

def neg_exponential_form(grp, beta, gamma, alpha=0, c=0):
    return alpha + gamma*(1 - np.exp(-(beta*grp)))

def exp_just_draw_v2(revenue_table, params_table, product_price=1, period=12, budg=2*10**9, grad=10**6, means=dict(), media_costs=dict()):
    opt_rev_dict = {}
    revenue_coefficients = pd.DataFrame(columns=['media', 'beta', 'gamma'])
    channels = [x for x in revenue_table.drop(
        columns='Investment').columns if x[-5:] != '_ROAS']

    for channel in channels:
        print(channel)
        delt = media_costs[media_costs['media'] == channel]['cost'].values[0]
        revenue_table[channel] = revenue_table[channel]*product_price
        grp = np.array(revenue_table['Investment'].values)
        ydata = np.array(revenue_table[channel].values)

        beta_start = float(params_table[params_table['feach_name']+params_table['coef_name'] == (
            channel+'__diminish_beta')]['value'].values[0])
        gamma_start = float(params_table[params_table['feach_name']+params_table['coef_name'] == (channel+'__diminish_gamma')]['value'].values[0])*float(
            params_table[params_table['feach_name']+params_table['coef_name'] == (channel+'__lm_coef')]['value'].values[0])
        if gamma_start < 0:
            gamma_start = -1*gamma_start
            
        for i in range(-5, 5, 1):
            scale = 10**(i)
            p0 = (beta_start/(scale*delt), gamma_start)
            popt, pcov = curve_fit(neg_exponential_form, grp, ydata, p0=p0, method='trf', bounds=(
                [0.000000000001, 0.0000000000001], [10000000, 100000000]), maxfev=10000000)
            resp = neg_exponential_form(
                np.array(range(0, budg, gran)), popt[0], popt[1], alpha=0, c=0)
            error = abs(sum(resp)-sum(ydata))/sum(ydata)
            if (error < 10**(-10)):
                break
        revenue_coefficients = revenue_coefficients.append(
            {'media': channel, 'beta': popt[0], 'gamma': popt[1]}, ignore_index=True)
    return revenue_coefficients

def optimal_budget_plot(optimised_budget):
	# x axis
	x = optimised_budget['budget']

	fig = go.Figure()

	media_cols = list(optimised_budget.drop(columns=['budget', 'profit']))

	# plot first media variable
	fig.add_trace(go.Scatter(
						    x=x,
						    y=optimised_budget[media_cols[0]],
						    mode='lines',
						    line=dict(width=0.5),
						    name=media_cols[0],
						    stackgroup='one',
						    groupnorm='percent'
						))
    
#     plot rest of media variables
	for col in media_cols[1:]:
		fig.add_trace(go.Scatter(
                                x=x,
                                y=optimised_budget[col],
                                mode='lines',
                                line=dict(width=0.5),
                                name=col,
                                stackgroup='one'
                            ))

#     set axis and labes
	fig.update_layout(
                    title='Optimal Budget Split',
                    xaxis_title='Budget',
                    yaxis_title='Budget Split Percentage',
                    showlegend=True,
                    xaxis=dict(
                                tickmode='auto',
                                nticks=10,
                                ticksuffix=' Rub.'),
                    yaxis=dict(
                                type='linear',
                                range=[1, 100],
                                ticksuffix='%')
                    )

	fig.show()
    
def resp_poly(revenue_table, col):
    xp = list(revenue_table['Investment'].values)
    fp = list(revenue_table[col].values)
#     fp = [np.exp(-1/(x+10**4)) for x in fp]
    min_a1_x, max_a1_x = min(xp), max(xp)
    new_a1_x = list(revenue_table['Investment'].values)
    a1_coefs = np.polyfit(xp, fp, 20)
    return(np.poly1d(a1_coefs))


def get_param_name(name, params):
    if '__lm_coef' in name:
        return('__lm_coef')
    if '__diminish_beta' in name:
        return('__diminish_beta')
    if '__diminish_gamma' in name:
        return('__diminish_gamma')
    if '__lambda_ad' in name:
        return('__lambda_ad')


def get_params_table(params):
    params_data = pd.DataFrame(
        columns=['feach_name', 'coef_name', 'value', 'min_val', 'max_val', 'vary'])

    for col in params.keys():
        coef_name = get_param_name(params[col].name, params)
        feach_name = params[col].name.replace(coef_name, '')
        value = params[col].value
        min_val = params[col].min
        max_val = params[col].max
        vary = params[col].vary
        line = [feach_name, coef_name, value, min_val, max_val, vary]
        row = pd.Series(line, ['feach_name', 'coef_name',
                               'value', 'min_val', 'max_val', 'vary'])
        params_data = params_data.append([row])

    return(params_data)

# Import dataset with sales and media
dataset = dataset=pd.read_csv('Media_data.csv', sep = ';').dropna()


# Import dataset with media costs data
media_costs=pd.DataFrame(columns=['media', 'cost', 'comment'])
media_costs['media']=['TV_1','TV_2','TV_3','TV_4','TV_5','TV_6','TV_7','TV_8','TV_9']
media_costs['cost']=[1,1,1,1,1,1,1,1,1]


dep_var=['Sales']
ad_vars=['TV_1','TV_2','TV_3','TV_4','TV_5','TV_6','TV_7','TV_8','TV_9', 'TV_competitor_1', 'TV_competitor_2', 'TV_competitor_3', 'TV_competitor_4']
market_vars=['baseline','Brand_price','Average_category_price','Press']
extra_vars = []
date='Week'

# dataset['Sales']=dataset['Sales']/1000
# dataset['TV_1']=dataset['TV_1']/100
# dataset['TV_2']=dataset['TV_2']/100
# dataset['TV_3']=dataset['TV_3']/100
# dataset['TV_4']=dataset['TV_4']/100
# dataset['TV_5']=dataset['TV_5']/100
# dataset['TV_6']=dataset['TV_6']/100
# dataset['TV_7']=dataset['TV_7']/100
# dataset['TV_8']=dataset['TV_8']/100
# dataset['TV_9']=dataset['TV_9']/100
# dataset['TV_competitor_1']=dataset['TV_competitor_1']/100
# dataset['TV_competitor_2']=dataset['TV_competitor_2']/100
# dataset['TV_competitor_3']=dataset['TV_competitor_3']/100
# dataset['TV_competitor_4']=dataset['TV_competitor_4']/100
# dataset['Press']=dataset['Press']/100
# dataset['Brand_price']=dataset['Brand_price']/100
# dataset['Average_category_price	']=dataset['Average_category_price']/100


X_train=mmm_pyton.MMM_dataset(dataset, dep_var, ad_vars, market_vars, extra_vars, date)
X_train_1=mmm_pyton.MMM_dataset(dataset, dep_var, ad_vars, market_vars, extra_vars, date)
y_train=X_train[dep_var[0]]
X_train=X_train.drop(columns=[dep_var[0]])

cols2impute = X_train.columns[(X_train.isnull().any() == True)]
cols2impute.values.tolist()

cols2diminish = X_train.columns[X_train.columns.str.contains('RF|TV|IMP')]
cols2diminish.values.tolist()

['baseline']
['baseline']

['TV_1',
 'TV_2',
 'TV_3',
 'TV_4',
 'TV_5',
 'TV_6',
 'TV_7',
 'TV_8',
 'TV_9',
 'TV_competitor_1',
 'TV_competitor_2',
 'TV_competitor_3',
 'TV_competitor_4']

# Scaling
means = {}
means[dep_var[0]] = y_train.mean()
y_train = y_train/y_train.mean()
for col in ad_vars:
    means[col] = X_train[col].mean()
    X_train[col] = X_train[col]/X_train[col].mean()
for col in [x for x in market_vars if x not in ['seasonality', 'weekend']]:
    means[col] = X_train[col].mean()
    X_train[col] = X_train[col]/X_train[col].mean()

if 'seasonality' in market_vars:
    means['seasonality'] = X_train['seasonality'].std()
    X_train['seasonality'] = X_train['seasonality'] / \
        X_train['seasonality'].std()

# Parameter space
params = Parameters()  

LAMBDA

for col in ad_vars:
    params.add(
        name=col + '__lambda_ad',
        value=0.3,
         min=0.1,
         max=0.6,
    #     vary=False
    )

BETA

for col in ad_vars:
    params.add(
        name = col + '__diminish_beta',
        value = 0.00055,
         min=0.00001,
         max=0.1,
    #     vary=False
    )

GAMMA

for col in ad_vars:
    params.add(
        name=col + '__diminish_gamma',
        value=1,
         min=0.0001,
         max=10,
         vary=False
    )

LINEAR MODEL COEF

for col in ad_vars:
    if 'competitor' in col:
        params.add(
            name=col + '__lm_coef', 
            value=1, 
            min=-1000,
            max=-0.0000001,
            vary=True
        )
    else:
        params.add(
            name=col + '__lm_coef', 
            value=1, 
            min=0.0000001,
            max=1000,
            vary=True
        )



for col in market_vars:
    params.add(
        name=col + '__lm_coef', 
        value=1,  
        min=-1000,
        max=1000,
        vary=True
    )

params

name	value	initial value	min	max	vary
TV_1__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_2__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_3__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_4__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_5__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_6__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_7__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_8__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_9__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_competitor_1__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_competitor_2__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_competitor_3__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_competitor_4__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_1__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_2__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_3__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_4__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_5__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_6__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_7__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_8__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_9__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_competitor_1__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_competitor_2__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_competitor_3__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_competitor_4__diminish_beta	5.5000e-04	0.00055	1.0000e-05	0.10000000	True
TV_1__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_2__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_3__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_4__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_5__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_6__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_7__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_8__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_9__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_competitor_1__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_competitor_2__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_competitor_3__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_competitor_4__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_1__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_2__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_3__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_4__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_5__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_6__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_7__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_8__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_9__lm_coef	1.00000000	1	1.0000e-07	1000.00000	True
TV_competitor_1__lm_coef	-1.0000e-07	1	-1000.00000	-1.0000e-07	True
TV_competitor_2__lm_coef	-1.0000e-07	1	-1000.00000	-1.0000e-07	True
TV_competitor_3__lm_coef	-1.0000e-07	1	-1000.00000	-1.0000e-07	True
TV_competitor_4__lm_coef	-1.0000e-07	1	-1000.00000	-1.0000e-07	True
baseline__lm_coef	1.00000000	1	-1000.00000	1000.00000	True
Brand_price__lm_coef	1.00000000	1	-1000.00000	1000.00000	True
Average_category_price__lm_coef	1.00000000	1	-1000.00000	1000.00000	True
Press__lm_coef	1.00000000	1	-1000.00000	1000.00000	True

result=mmm_pyton.model(params,cols2impute,cols2diminish,X_train,y_train,maxiter=150)

| niter |f evals|CG iter|  obj func   |tr radius |   opt    |  c viol  | penalty  |CG stop|
|-------|-------|-------|-------------|----------|----------|----------|----------|-------|
|   1   |  44   |   0   | +1.5653e+03 | 1.00e+00 | 1.45e+06 | 0.00e+00 | 1.00e+00 |   0   |
|   2   |  88   |   1   | +1.5653e+03 | 1.00e-01 | 1.45e+06 | 0.00e+00 | 1.00e+00 |   2   |
|   3   |  132  |   3   | +1.3776e+02 | 1.00e-01 | 4.89e+05 | 0.00e+00 | 1.00e+00 |   4   |
|   4   |  176  |   5   | +1.8785e+01 | 1.00e-01 | 9.04e+04 | 0.00e+00 | 1.00e+00 |   4   |
|   5   |  220  |   7   | +6.9447e+00 | 1.00e-01 | 2.13e+04 | 0.00e+00 | 1.00e+00 |   4   |
|   6   |  264  |   9   | +5.6551e+00 | 1.00e-01 | 1.83e+04 | 0.00e+00 | 1.00e+00 |   4   |
|   7   |  308  |  11   | +5.0898e+00 | 1.00e-01 | 3.08e+03 | 0.00e+00 | 1.00e+00 |   4   |
|   8   |  352  |  14   | +5.0843e+00 | 1.00e-01 | 5.63e+02 | 0.00e+00 | 1.00e+00 |   4   |
|   9   |  396  |  17   | +5.0838e+00 | 1.00e-01 | 5.01e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  10   |  440  |  20   | +5.0826e+00 | 1.00e-01 | 8.21e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  11   |  484  |  23   | +5.0795e+00 | 1.00e-01 | 1.81e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  12   |  528  |  27   | +5.0724e+00 | 1.00e-01 | 3.19e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  13   |  572  |  31   | +5.0582e+00 | 1.00e-01 | 4.52e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  14   |  616  |  35   | +5.0385e+00 | 1.00e-01 | 4.57e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  15   |  660  |  39   | +5.0244e+00 | 1.00e-01 | 2.57e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  16   |  704  |  43   | +5.0203e+00 | 1.00e-01 | 5.88e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  17   |  748  |  47   | +5.0199e+00 | 1.00e-01 | 2.11e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  18   |  792  |  52   | +5.0198e+00 | 1.00e-01 | 2.56e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  19   |  836  |  57   | +5.0196e+00 | 1.00e-01 | 3.28e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  20   |  880  |  62   | +5.0190e+00 | 1.00e-01 | 4.63e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  21   |  924  |  67   | +5.0173e+00 | 1.00e-01 | 8.08e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  22   |  968  |  72   | +5.0133e+00 | 1.00e-01 | 1.32e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  23   | 1012  |  77   | +5.0037e+00 | 1.00e-01 | 2.03e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  24   | 1056  |  82   | +4.9841e+00 | 1.00e-01 | 2.72e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  25   | 1100  |  87   | +4.9552e+00 | 1.00e-01 | 2.74e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  26   | 1144  |  92   | +4.9323e+00 | 1.00e-01 | 1.60e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  27   | 1188  |  97   | +4.9247e+00 | 1.00e-01 | 3.70e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  28   | 1232  |  102  | +4.9240e+00 | 1.00e-01 | 2.53e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  29   | 1276  |  107  | +4.9240e+00 | 1.00e-01 | 3.22e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  30   | 1320  |  113  | +4.9240e+00 | 1.00e-02 | 3.22e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  31   | 1364  |  119  | +4.9240e+00 | 1.00e-03 | 3.22e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  32   | 1408  |  125  | +4.9240e+00 | 1.00e-04 | 3.22e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  33   | 1452  |  131  | +4.9240e+00 | 1.00e-05 | 3.22e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  34   | 1496  |  137  | +4.9240e+00 | 1.71e-06 | 3.22e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  35   | 1540  |  139  | +4.9240e+00 | 1.71e-06 | 2.32e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  36   | 1584  |  143  | +4.9240e+00 | 3.42e-06 | 1.39e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  37   | 1628  |  148  | +4.9240e+00 | 2.40e-05 | 1.07e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  38   | 1672  |  154  | +4.9240e+00 | 1.68e-04 | 4.02e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  39   | 1716  |  160  | +4.9238e+00 | 1.17e-03 | 1.78e+02 | 0.00e+00 | 1.00e+00 |   2   |
|  40   | 1760  |  165  | +4.9238e+00 | 1.17e-03 | 1.29e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  41   | 1804  |  173  | +4.9228e+00 | 3.94e-03 | 2.36e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  42   | 1848  |  181  | +4.9172e+00 | 2.76e-02 | 4.50e+02 | 0.00e+00 | 1.00e+00 |   2   |
|  43   | 1892  |  189  | +4.9168e+00 | 2.76e-02 | 3.04e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  44   | 1936  |  197  | +4.9164e+00 | 2.76e-02 | 3.72e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  45   | 1980  |  206  | +4.8756e+00 | 1.93e-01 | 3.07e+02 | 0.00e+00 | 1.00e+00 |   2   |
|  46   | 2024  |  214  | +4.8750e+00 | 1.93e-01 | 6.93e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  47   | 2068  |  223  | +4.5933e+00 | 1.35e+00 | 2.42e+03 | 0.00e+00 | 1.00e+00 |   2   |
|  48   | 2112  |  231  | +4.5795e+00 | 1.35e+00 | 1.92e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  49   | 2156  |  241  | +3.8350e+00 | 2.09e+00 | 5.88e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  50   | 2200  |  249  | +3.7796e+00 | 2.09e+00 | 2.48e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  51   | 2244  |  257  | +3.7674e+00 | 2.09e+00 | 1.07e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  52   | 2288  |  267  | +3.7674e+00 | 2.09e-01 | 1.07e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  53   | 2332  |  277  | +3.7673e+00 | 2.09e-01 | 4.55e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  54   | 2376  |  287  | +3.7672e+00 | 2.09e-01 | 4.57e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  55   | 2420  |  298  | +3.7381e+00 | 2.09e-01 | 2.60e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  56   | 2464  |  304  | +3.7250e+00 | 2.09e-01 | 9.90e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  57   | 2508  |  315  | +3.6540e+00 | 2.09e-01 | 9.04e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  58   | 2552  |  321  | +3.6524e+00 | 2.09e-01 | 8.33e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  59   | 2596  |  332  | +3.6456e+00 | 2.09e-01 | 2.94e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  60   | 2640  |  335  | +3.6455e+00 | 2.09e-01 | 1.86e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  61   | 2684  |  346  | +3.6451e+00 | 2.09e-01 | 1.08e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  62   | 2728  |  352  | +3.6451e+00 | 2.09e-01 | 1.84e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  63   | 2772  |  354  | +3.6451e+00 | 2.09e-01 | 1.84e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  64   | 2816  |  358  | +3.6451e+00 | 2.09e-01 | 9.87e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  65   | 2860  |  363  | +3.6451e+00 | 2.09e-01 | 2.02e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  66   | 2904  |  368  | +3.6451e+00 | 2.09e-01 | 4.00e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  67   | 2948  |  373  | +3.6451e+00 | 2.09e-01 | 7.01e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  68   | 2992  |  379  | +3.6451e+00 | 2.09e-01 | 1.20e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  69   | 3036  |  385  | +3.6451e+00 | 2.09e-01 | 2.00e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  70   | 3080  |  391  | +3.6451e+00 | 2.09e-01 | 3.30e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  71   | 3124  |  394  | +3.6451e+00 | 2.09e-01 | 2.64e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  72   | 3168  |  402  | +3.6446e+00 | 2.09e-01 | 4.41e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  73   | 3212  |  412  | +3.6412e+00 | 2.09e-01 | 1.27e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  74   | 3256  |  415  | +3.6406e+00 | 2.09e-01 | 8.02e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  75   | 3300  |  425  | +3.6259e+00 | 2.09e-01 | 2.69e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  76   | 3344  |  441  | +3.5445e+00 | 2.09e-01 | 4.90e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  77   | 3388  |  449  | +3.5173e+00 | 2.09e-01 | 2.03e+03 | 0.00e+00 | 1.00e+00 |   4   |
|  78   | 3432  |  457  | +3.5145e+00 | 2.09e-01 | 3.51e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  79   | 3476  |  468  | +3.4966e+00 | 2.09e-01 | 1.10e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  80   | 3520  |  479  | +3.4869e+00 | 2.09e-01 | 1.19e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  81   | 3564  |  485  | +3.4869e+00 | 2.09e-01 | 2.03e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  82   | 3608  |  493  | +3.4869e+00 | 2.09e-02 | 2.03e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  83   | 3652  |  501  | +3.4869e+00 | 2.09e-03 | 2.03e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  84   | 3696  |  510  | +3.4869e+00 | 2.09e-04 | 2.03e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  85   | 3740  |  519  | +3.4869e+00 | 2.09e-05 | 2.03e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  86   | 3784  |  527  | +3.4869e+00 | 2.09e-05 | 1.03e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  87   | 3828  |  534  | +3.4869e+00 | 1.46e-04 | 2.02e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  88   | 3872  |  544  | +3.4868e+00 | 4.10e-04 | 3.71e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  89   | 3916  |  554  | +3.4867e+00 | 1.19e-03 | 6.61e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  90   | 3960  |  564  | +3.4864e+00 | 3.14e-03 | 1.11e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  91   | 4004  |  570  | +3.4862e+00 | 3.14e-03 | 8.76e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  92   | 4048  |  580  | +3.4829e+00 | 1.42e-02 | 2.71e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  93   | 4092  |  592  | +3.4698e+00 | 9.93e-02 | 2.53e+02 | 0.00e+00 | 1.00e+00 |   2   |
|  94   | 4136  |  600  | +3.4686e+00 | 9.93e-02 | 9.91e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  95   | 4180  |  606  | +3.4683e+00 | 9.93e-02 | 5.87e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  96   | 4224  |  622  | +3.4555e+00 | 1.69e-01 | 7.28e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  97   | 4268  |  628  | +3.4555e+00 | 1.69e-01 | 5.80e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  98   | 4312  |  651  | +3.4488e+00 | 1.95e-01 | 7.88e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  99   | 4356  |  657  | +3.4488e+00 | 1.95e-01 | 5.60e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  100  | 4400  |  668  | +3.4481e+00 | 1.95e-01 | 8.97e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  101  | 4444  |  671  | +3.4481e+00 | 1.95e-01 | 6.30e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  102  | 4488  |  682  | +3.4480e+00 | 1.95e-01 | 9.18e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  103  | 4532  |  688  | +3.4480e+00 | 1.95e-02 | 9.18e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  104  | 4576  |  694  | +3.4480e+00 | 1.95e-03 | 9.18e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  105  | 4620  |  701  | +3.4480e+00 | 1.95e-04 | 9.18e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  106  | 4664  |  707  | +3.4480e+00 | 1.95e-04 | 1.85e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  107  | 4708  |  715  | +3.4480e+00 | 1.95e-04 | 4.46e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  108  | 4752  |  720  | +3.4480e+00 | 1.95e-04 | 3.55e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  109  | 4796  |  728  | +3.4480e+00 | 1.95e-04 | 1.59e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  110  | 4840  |  735  | +3.4479e+00 | 1.37e-03 | 6.30e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  111  | 4884  |  743  | +3.4479e+00 | 1.37e-03 | 5.13e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  112  | 4928  |  754  | +3.4474e+00 | 4.89e-03 | 1.57e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  113  | 4972  |  759  | +3.4473e+00 | 4.89e-03 | 7.94e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  114  | 5016  |  767  | +3.4473e+00 | 4.89e-03 | 1.39e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  115  | 5060  |  778  | +3.4443e+00 | 3.00e-02 | 9.92e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  116  | 5104  |  786  | +3.4442e+00 | 3.00e-02 | 3.02e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  117  | 5148  |  797  | +3.4367e+00 | 1.27e-01 | 1.15e+02 | 0.00e+00 | 1.00e+00 |   4   |
|  118  | 5192  |  805  | +3.4367e+00 | 1.27e-01 | 3.51e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  119  | 5236  |  836  | +3.4334e+00 | 1.48e-01 | 6.25e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  120  | 5280  |  839  | +3.4334e+00 | 1.48e-01 | 4.28e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  121  | 5324  |  855  | +3.4331e+00 | 1.48e-01 | 1.90e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  122  | 5368  |  860  | +3.4331e+00 | 1.48e-01 | 2.75e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  123  | 5412  |  872  | +3.4330e+00 | 1.48e-01 | 1.69e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  124  | 5456  |  875  | +3.4330e+00 | 1.48e-01 | 2.56e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  125  | 5500  |  887  | +3.4330e+00 | 1.48e-01 | 1.39e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  126  | 5544  |  889  | +3.4330e+00 | 1.48e-02 | 1.39e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  127  | 5588  |  891  | +3.4330e+00 | 1.48e-03 | 1.39e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  128  | 5632  |  894  | +3.4330e+00 | 1.48e-04 | 1.39e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  129  | 5676  |  899  | +3.4330e+00 | 1.48e-05 | 1.39e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  130  | 5720  |  904  | +3.4330e+00 | 1.48e-06 | 1.39e+00 | 0.00e+00 | 1.00e+00 |   4   |
|  131  | 5764  |  909  | +3.4330e+00 | 7.38e-07 | 1.39e+00 | 0.00e+00 | 1.00e+00 |   2   |
|  132  | 5808  |  912  | +3.4330e+00 | 1.48e-06 | 7.35e+00 | 0.00e+00 | 1.00e+00 |   2   |
|  133  | 5852  |  917  | +3.4330e+00 | 1.03e-05 | 1.17e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  134  | 5896  |  925  | +3.4330e+00 | 7.23e-05 | 5.06e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  135  | 5940  |  928  | +3.4330e+00 | 7.23e-05 | 3.38e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  136  | 5984  |  932  | +3.4330e+00 | 7.23e-05 | 3.45e-01 | 0.00e+00 | 1.00e+00 |   4   |
|  137  | 6028  |  944  | +3.4330e+00 | 3.11e-04 | 1.92e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  138  | 6072  |  955  | +3.4328e+00 | 2.18e-03 | 8.21e+01 | 0.00e+00 | 1.00e+00 |   2   |
|  139  | 6116  |  959  | +3.4328e+00 | 2.18e-03 | 5.25e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  140  | 6160  |  970  | +3.4328e+00 | 2.18e-04 | 5.25e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  141  | 6204  |  981  | +3.4328e+00 | 2.18e-05 | 5.25e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  142  | 6248  |  992  | +3.4328e+00 | 4.51e-06 | 5.25e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  143  | 6292  | 1002  | +3.4328e+00 | 2.26e-06 | 5.25e+01 | 0.00e+00 | 1.00e+00 |   4   |
|  144  | 6336  | 1012  | +3.4328e+00 | 4.51e-06 | 6.58e+00 | 0.00e+00 | 1.00e+00 |   2   |
|  145  | 6380  | 1022  | +3.4328e+00 | 1.87e-06 | 6.58e+00 | 0.00e+00 | 1.00e+00 |   2   |
|  146  | 6424  | 1032  | +3.4328e+00 | 7.77e-07 | 6.58e+00 | 0.00e+00 | 1.00e+00 |   2   |
|  147  | 6468  | 1042  | +3.4328e+00 | 2.40e-07 | 6.58e+00 | 0.00e+00 | 1.00e+00 |   2   |
|  148  | 6512  | 1048  | +3.4328e+00 | 9.25e-08 | 6.58e+00 | 0.00e+00 | 1.00e+00 |   2   |
|  149  | 6556  | 1054  | +3.4328e+00 | 4.62e-08 | 6.58e+00 | 0.00e+00 | 1.00e+00 |   2   |
|  150  | 6600  | 1059  | +3.4328e+00 | 9.25e-08 | 2.46e+00 | 0.00e+00 | 1.00e+00 |   2   |

The maximum number of function evaluations is exceeded.
Number of iterations: 150, function evaluations: 6600, CG iterations: 1059, optimality: 2.46e+00, constraint violation: 0.00e+00, execution time: 2e+02 s.

result

Fit Statistics

fitting method	equality_constrained_sqp
# function evals	6600
# data points	139
# variables	43
chi-square	3.43279935
reduced chi-square	0.03575833
Akaike info crit.	-428.452604
Bayesian info crit.	-302.270225

Variables

name	value	initial value	min	max	vary
TV_1__lambda_ad	0.30303699	0.3	0.10000000	0.60000000	True
TV_2__lambda_ad	0.30089219	0.3	0.10000000	0.60000000	True
TV_3__lambda_ad	0.29986129	0.3	0.10000000	0.60000000	True
TV_4__lambda_ad	0.30425889	0.3	0.10000000	0.60000000	True
TV_5__lambda_ad	0.29971337	0.3	0.10000000	0.60000000	True
TV_6__lambda_ad	0.29990602	0.3	0.10000000	0.60000000	True
TV_7__lambda_ad	0.29964113	0.3	0.10000000	0.60000000	True
TV_8__lambda_ad	0.30019051	0.3	0.10000000	0.60000000	True
TV_9__lambda_ad	0.29972196	0.3	0.10000000	0.60000000	True
TV_competitor_1__lambda_ad	0.29999940	0.3	0.10000000	0.60000000	True
TV_competitor_2__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_competitor_3__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_competitor_4__lambda_ad	0.30000000	0.3	0.10000000	0.60000000	True
TV_1__diminish_beta	0.00209366	0.00055	1.0000e-05	0.10000000	True
TV_2__diminish_beta	7.6947e-04	0.00055	1.0000e-05	0.10000000	True
TV_3__diminish_beta	6.7866e-04	0.00055	1.0000e-05	0.10000000	True
TV_4__diminish_beta	0.00163076	0.00055	1.0000e-05	0.10000000	True
TV_5__diminish_beta	7.9730e-05	0.00055	1.0000e-05	0.10000000	True
TV_6__diminish_beta	1.3213e-04	0.00055	1.0000e-05	0.10000000	True
TV_7__diminish_beta	4.5607e-04	0.00055	1.0000e-05	0.10000000	True
TV_8__diminish_beta	1.1493e-05	0.00055	1.0000e-05	0.10000000	True
TV_9__diminish_beta	4.5981e-04	0.00055	1.0000e-05	0.10000000	True
TV_competitor_1__diminish_beta	5.4782e-04	0.00055	1.0000e-05	0.10000000	True
TV_competitor_2__diminish_beta	5.5200e-04	0.00055	1.0000e-05	0.10000000	True
TV_competitor_3__diminish_beta	5.5172e-04	0.00055	1.0000e-05	0.10000000	True
TV_competitor_4__diminish_beta	5.4562e-04	0.00055	1.0000e-05	0.10000000	True
TV_1__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_2__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_3__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_4__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_5__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_6__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_7__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_8__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_9__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_competitor_1__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_competitor_2__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_competitor_3__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_competitor_4__diminish_gamma	1.00000000	1	1.0000e-04	10.0000000	False
TV_1__lm_coef	22.1180701	1	1.0000e-07	1000.00000	True
TV_2__lm_coef	7.33799577	1	1.0000e-07	1000.00000	True
TV_3__lm_coef	3.82560201	1	1.0000e-07	1000.00000	True
TV_4__lm_coef	23.6269004	1	1.0000e-07	1000.00000	True
TV_5__lm_coef	0.65059427	1	1.0000e-07	1000.00000	True
TV_6__lm_coef	0.32506329	1	1.0000e-07	1000.00000	True
TV_7__lm_coef	0.24837866	1	1.0000e-07	1000.00000	True
TV_8__lm_coef	19.0971454	1	1.0000e-07	1000.00000	True
TV_9__lm_coef	0.17235058	1	1.0000e-07	1000.00000	True
TV_competitor_1__lm_coef	-4.7665e-05	-1e-07	-1000.00000	-1.0000e-07	True
TV_competitor_2__lm_coef	-2.5112e-04	-1e-07	-1000.00000	-1.0000e-07	True
TV_competitor_3__lm_coef	-1.3420e-05	-1e-07	-1000.00000	-1.0000e-07	True
TV_competitor_4__lm_coef	-4.7949e-06	-1e-07	-1000.00000	-1.0000e-07	True
baseline__lm_coef	0.26657679	1	-1000.00000	1000.00000	True
Brand_price__lm_coef	-0.42784802	1	-1000.00000	1000.00000	True
Average_category_price__lm_coef	1.04825171	1	-1000.00000	1000.00000	True
Press__lm_coef	0.01988647	1	-1000.00000	1000.00000	True

r2_score(y_train, mmm_pyton.get_prediction(result.params.valuesdict(), X_train, cols2impute, cols2diminish))

0.41779431116996746

# Estimate impact sizes with pretrained model
decomposition_df_sshape = mmm_pyton.model_dt(
    result, X_train, y_train, cols2impute, ad_vars)

# Plot the decomposition
for col in decomposition_df_sshape.columns:
    decomposition_df_sshape[col] = decomposition_df_sshape[col] * \
        means[dep_var[0]]
params_sshape = result.params
mmm_pyton.decomposition(decomposition_df_sshape)

# Calculate metrics and statistics
r2_sshape = r2_score(
    decomposition_df_sshape['actual'].values, decomposition_df_sshape['fitted'].values)
ad_r2_sshape = 1-(1-r2_sshape)*(len(y_train)-1) / \
    (len(y_train)-X_train.shape[1]-1)
# pvalue_sshape_table=mmm_python.decomp_stat_calc(decomposition_df_sshape[clicks+['actual','fitted']])

# Print model metrices
print('R-squared: ' + str(np.round(r2_sshape*100, 1)) + '%')
print('Adjusted R-squared: ' + str(np.round(ad_r2_sshape*100, 1)) + '%')
# display(pvalue_sshape_table)

R-squared: 41.8%
Adjusted R-squared: 33.6%

best_params=result.params.valuesdict()

means

{'Sales': 10217.510791366907,
 'TV_1': 12.496402877697841,
 'TV_2': 1.9640287769784173,
 'TV_3': 2.035971223021583,
 'TV_4': 7.705035971223022,
 'TV_5': 0.5179856115107914,
 'TV_6': 0.381294964028777,
 'TV_7': 0.30935251798561153,
 'TV_8': 0.2014388489208633,
 'TV_9': 0.41007194244604317,
 'TV_competitor_1': 5.517985611510792,
 'TV_competitor_2': 2.0863309352517985,
 'TV_competitor_3': 3.7697841726618706,
 'TV_competitor_4': 3.697841726618705,
 'baseline': 1.0,
 'Brand_price': 72.4820143884892,
 'Average_category_price': 123.67625899280576,
 'Press': 13.827338129496402}

product_price=10217*123
budg=3*10**8
revenue_table=mmm_pyton.direct_response_curves(budg,best_params,media_costs,period=52)

# import importlib
# importlib.reload(mmm_pyton)

revenue_table=mmm_pyton.response_curves_plot(revenue_table)

mmm_pyton.ROAS_curves_plot(revenue_table, budg, product_price)

# Create params table
params_table = get_params_table(params)
params_table

	feach_name	coef_name	value	min_val	max_val	vary
0	TV_1	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_2	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_3	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_4	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_5	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_6	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_7	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_8	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_9	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_competitor_1	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_competitor_2	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_competitor_3	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_competitor_4	__lambda_ad	3.000000e-01	1.000000e-01	6.000000e-01	True
0	TV_1	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_2	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_3	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_4	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_5	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_6	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_7	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_8	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_9	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_competitor_1	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_competitor_2	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_competitor_3	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_competitor_4	__diminish_beta	5.500000e-04	1.000000e-05	1.000000e-01	True
0	TV_1	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_2	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_3	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_4	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_5	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_6	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_7	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_8	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_9	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_competitor_1	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_competitor_2	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_competitor_3	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_competitor_4	__diminish_gamma	1.000000e+00	1.000000e-04	1.000000e+01	False
0	TV_1	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_2	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_3	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_4	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_5	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_6	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_7	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_8	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_9	__lm_coef	1.000000e+00	1.000000e-07	1.000000e+03	True
0	TV_competitor_1	__lm_coef	-1.000000e-07	-1.000000e+03	-1.000000e-07	True
0	TV_competitor_2	__lm_coef	-1.000000e-07	-1.000000e+03	-1.000000e-07	True
0	TV_competitor_3	__lm_coef	-1.000000e-07	-1.000000e+03	-1.000000e-07	True
0	TV_competitor_4	__lm_coef	-1.000000e-07	-1.000000e+03	-1.000000e-07	True
0	baseline	__lm_coef	1.000000e+00	-1.000000e+03	1.000000e+03	True
0	Brand_price	__lm_coef	1.000000e+00	-1.000000e+03	1.000000e+03	True
0	Average_category_price	__lm_coef	1.000000e+00	-1.000000e+03	1.000000e+03	True
0	Press	__lm_coef	1.000000e+00	-1.000000e+03	1.000000e+03	True

gran = 1000000
model_type = 'exp'

revenue_coefficients = exp_just_draw_v2(revenue_table, params_table, product_price=1, period=12, budg=budg, grad=10**4, means=means, media_costs=media_costs)
# revenue_coefficients=exp_just_draw_v2(revenue_table_val, params_table, product_price=1, period=1, budg=budg_upd, grad=10**4, means=means, media_costs=media_costs)
media_vars = revenue_coefficients['media'].tolist()

resp_func_dict = {}
for col in media_vars:
    resp_func_dict[col] = resp_poly(revenue_table, col)

    # Bounds for x
bounds = Bounds(np.repeat(0, len(media_vars)), np.repeat(1, len(media_vars)))

# x start values
x0 = list(np.repeat(0.01/len(media_vars), len(media_vars)))

# Media vars columns
columns = revenue_coefficients['media'].tolist()
columns.insert(0, 'budget')
columns.insert(len(columns), 'profit')

# DF to fill out by optimization function
optimised_budget = pd.DataFrame(columns=columns)

# Row number of optimised_budget DF
row_n = 0
# Return DF with optimisation results
# for budggg in range(0, int(sum(sat_dict.values())/10**4)): # set maximum investments in millions
for budggg in range(1, 300):  # set maximum investments in millions
    print(budggg)
    row = []
    budget = budggg*(10**5)

    row.append(budget)

    x0 = list(np.repeat(0.01/len(media_vars), len(media_vars)))

    
    
    def optimum_func():
        optimum = pysolnp.solve(
            obj_func=optimize_budget,
            par_start_value=x0,
            par_lower_limit=list(np.repeat(0, len(media_vars))),
            par_upper_limit=list(np.repeat(1, len(media_vars))),
            eq_func=cons_f,
            eq_values=[1],
            max_major_iter=10000,
            max_minor_iter=10000)
        return(optimum)

    def optimize_budget(x):
        revenue = []

        # Здесь надо посоветоваться, ведь мы сразу годовой бюджет в модель пихаем, а обучалось на месяцах
        # Calculate revenues for all channels -> sum it up
#         print(budget)
        if model_type == 'exp':
#             print(x)
            for i, col in list(zip(range(len(media_vars)), media_vars)):
                # Calculate revenue for the channel

                revenue.append(resp_func_dict[col](budget * x[i]))
    #             revenue.append(build_poly(budget * x[i],resp_func_dict[col]))
    #             revenue.append(x[i]**2)

        revenue = sum(revenue)
#         print(revenue)
        # Set optimisation function
        return -(revenue)

    def cons_f(x):
        return [sum(x)]

    res = optimum_func()

    for x in res.optimum:
        row.append(x*budggg)
    
    row.append(res.solve_value)
    optimised_budget.loc[row_n] = row

    row_n += 1

optimised_budget['profit'] = -optimised_budget['profit']

TV_1
TV_2
TV_3
TV_4
TV_5
TV_6
TV_7
TV_8
TV_9
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optimal_budget_plot(optimised_budget.fillna(method='ffill'))

opt_rev_plot(optimised_budget)

pip install streamlit

Collecting streamlit
  Downloading streamlit-0.88.0-py2.py3-none-any.whl (8.0 MB)
     |████████████████████████████████| 8.0 MB 4.7 MB/s eta 0:00:01
Requirement already satisfied: tornado>=5.0 in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (6.1)
Requirement already satisfied: pandas>=0.21.0 in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (1.2.4)
Collecting pyarrow
  Downloading pyarrow-5.0.0-cp38-cp38-macosx_10_13_x86_64.whl (17.6 MB)
     |████████████████████████████████| 17.6 MB 4.5 MB/s eta 0:00:01
Collecting validators
  Downloading validators-0.18.2-py3-none-any.whl (19 kB)
Requirement already satisfied: attrs in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (21.2.0)
Collecting blinker
  Downloading blinker-1.4.tar.gz (111 kB)
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Requirement already satisfied: numpy in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (1.19.5)
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Requirement already satisfied: cachetools>=4.0 in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (4.2.2)
Collecting altair>=3.2.0
  Downloading altair-4.1.0-py3-none-any.whl (727 kB)
     |████████████████████████████████| 727 kB 6.5 MB/s eta 0:00:01
Requirement already satisfied: requests in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (2.25.1)
Collecting astor
  Downloading astor-0.8.1-py2.py3-none-any.whl (27 kB)
Requirement already satisfied: pillow>=6.2.0 in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (8.2.0)
Requirement already satisfied: python-dateutil in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (2.8.1)
Collecting base58
  Downloading base58-2.1.0-py3-none-any.whl (5.6 kB)
Collecting tzlocal
  Downloading tzlocal-3.0-py3-none-any.whl (16 kB)
Requirement already satisfied: protobuf!=3.11,>=3.6.0 in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from streamlit) (3.16.0)
Collecting pydeck>=0.1.dev5
  Downloading pydeck-0.7.0-py2.py3-none-any.whl (4.3 MB)
     |████████████████████████████████| 4.3 MB 6.1 MB/s eta 0:00:01
Collecting click<8.0,>=7.0
  Downloading click-7.1.2-py2.py3-none-any.whl (82 kB)
     |████████████████████████████████| 82 kB 2.1 MB/s eta 0:00:011
Collecting toml
  Downloading toml-0.10.2-py2.py3-none-any.whl (16 kB)
Collecting gitpython!=3.1.19
  Downloading GitPython-3.1.18-py3-none-any.whl (170 kB)
     |████████████████████████████████| 170 kB 5.1 MB/s eta 0:00:01
Requirement already satisfied: entrypoints in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from altair>=3.2.0->streamlit) (0.3)
Requirement already satisfied: jinja2 in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from altair>=3.2.0->streamlit) (3.0.0)
Collecting toolz
  Downloading toolz-0.11.1-py3-none-any.whl (55 kB)
     |████████████████████████████████| 55 kB 4.3 MB/s eta 0:00:01
Requirement already satisfied: jsonschema in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from altair>=3.2.0->streamlit) (3.2.0)
Collecting gitdb<5,>=4.0.1
  Downloading gitdb-4.0.7-py3-none-any.whl (63 kB)
     |████████████████████████████████| 63 kB 4.0 MB/s  eta 0:00:01
Collecting smmap<5,>=3.0.1
  Downloading smmap-4.0.0-py2.py3-none-any.whl (24 kB)
Requirement already satisfied: pytz>=2017.3 in /Users/sokolov/opt/anaconda3/lib/python3.8/site-packages (from pandas>=0.21.0->streamlit) (2021.1)
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Collecting backports.zoneinfo
  Downloading backports.zoneinfo-0.2.1-cp38-cp38-macosx_10_14_x86_64.whl (35 kB)
Building wheels for collected packages: blinker
  Building wheel for blinker (setup.py) ... done
  Created wheel for blinker: filename=blinker-1.4-py3-none-any.whl size=13451 sha256=ce7509e9a90ce5e78ae0766b3bcf562cb474d949dbc888d627e6940ec718aefa
  Stored in directory: /Users/sokolov/Library/Caches/pip/wheels/b7/a5/68/fe632054a5eadd531c7a49d740c50eb6adfbeca822b4eab8d4
Successfully built blinker
Installing collected packages: smmap, toolz, gitdb, backports.zoneinfo, validators, tzlocal, toml, pydeck, pyarrow, gitpython, click, blinker, base58, astor, altair, streamlit
  Attempting uninstall: click
    Found existing installation: click 8.0.1
    Uninstalling click-8.0.1:
      Successfully uninstalled click-8.0.1
Successfully installed altair-4.1.0 astor-0.8.1 backports.zoneinfo-0.2.1 base58-2.1.0 blinker-1.4 click-7.1.2 gitdb-4.0.7 gitpython-3.1.18 pyarrow-5.0.0 pydeck-0.7.0 smmap-4.0.0 streamlit-0.88.0 toml-0.10.2 toolz-0.11.1 tzlocal-3.0 validators-0.18.2
Note: you may need to restart the kernel to use updated packages.